Using a distributed algorithm rather than a centralized one can be extremely beneficial in large search problems. In addition, the incorporation of machine learning techniques like Reinforcement Learning (RL) into search algorithms has often been found to improve their performance. In this article we investigate a search algorithm that combines these properties by employing RL in a distributed manner, essentially using the team game approach. We then present bi-utility search, which interleaves our distributed algorithm with (centralized) simulated annealing, by using the distributed algorithm to guide the exploration step of the simulated annealing. We investigate using these algorithms in the domain of minimizing the loss of importance-weighted communication data traversing a constellations of communication satellites. To do this we introduce the idea of running these algorithms "on top" of an underlying, learning-free routing algorithm. They do this by having the actions ...